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The square roots of perfect squares are the numbers that when squared create perfect squares as for example 36 is a perfect square and its square root is 6 which when squared is 36

Q: What is the relationship between perfect squares and square roots?

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There are 24 perfect squares between 50 and 1000.

The square root of every perfect square is an integer. However, there are also square roots of numbers that are not perfect squares.

100 is a perfect square of 10.The square root of 1000 is 31.6blahblahblah, so the square of 31 is less than 1000 and the square of 32 is more than 1000.That means the perfect squares between (not including) 100 and 1000 are the squares of 11 through 31, a total of 21 different values.

The smallest perfect squares that end with 9 are 9 (the square of 3) 49 (the square of 7). Their difference is 40.

Find the perfect squares that your number lies between. Your square root will lie between their square roots. Whichever it is closer to will indicate the size of the decimal.

No. There are infinitely many perfect squares so there is no "the" perfect square.

No. Convention defines perfect squares as squares of positive integers.

There is a partial relationship. The principal square root of a perfect square is the number itself. For example, the principal square root of 5^2 = the principal square root of 25 = the positive element in {-5, 5} = 5. The converse is not true. The number 3, for example, has a square root which are approx -1.7321 and 1.7321. But the square of either of these numbers is 3, but that is not a perfect square since it is not the square of an integer.

No- the closest perfect squares are 36 (perfect square of 6) and 49 (perfect square of 7)

No, 188 is not a perfect square. The nearest perfect squares as 169 and 196.

That the set of perfect squares is closed under multiplication. That is if x and y are any two perfect squares, then x*y is a perfect square.

The square root of 3000 is 54.77 and the square root of 3200 is 56.57. So the only perfect squares in the required number range are 552 = 3025 and 562 = 3126.